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In this paper, we study a generalized Zakharov-Kuznetsov equation in three variables, which has applications in the nonlinear development of ion-acoustic waves in a magnetized plasma. Conservation laws for this equation are constructed for the first time by using the new conservation theorem of Ibragimov. Furthermore, new exact solutions are obtained by employing the Lie symmetry method along with the simplest equation method.doi:10.3390/sym7020949 fatcat:owzs53eg3vdgbmprr4bfa65z2a